Teacher Tune-ups are concise explanations prepared for teachers by math experts.

Teachers raise GREAT questions about mathematics! Select from those listed below to read a response from a math educator or mathematician. To recommend an additional Teacher Tune-up, complete the form at the bottom of this page.

Ratio and Proportional Relationships

What's the difference between a ratio and a fraction, and why should I care?

What are the shortcomings of cross-multiplication?

What is unit rate as opposed to rate?

How is "scaling" related to proportional relationships?

Number Systems

Number Line Models for Sums and Differences with Integers

Difference, Distance, and the Truth about Absolute Value

What are the three basic ways we think of division?

Making Sense of Division of Fractions

Delaying "Invert and Multiply"

Multiplication makes things bigger and division makes things smaller, right? Well, not so fast...

Expressions and Equations

The Algebraic Alphabet: Unknowns, Variables, and Parameters

How do you generate equations from patterns?

Algebraic Terms Sixth and Seventh Graders Encounter

What are ways to represent different start points and different speeds?

How can focusing on expressions prevent students from rushing to answer-getting?

Geometry

What is a net? What can you learn from a net?

Drawing Triangles: Conventions and Mechanics

Statistics and Probability

How should students describe the center and spread of a data set?

We use dot plots, histograms, and box plots...which one to use?

Probability Basics for Middle-School Teachers

Variability and Randomness within Classroom Activities

Do you have a suggestion for an additional Teacher Tune-up?

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